Answer

Verified

20.4k+ views

**Hint:**A quantity that can be measured in terms of numerical values and can be expressed in terms of numerical values is called a physical quantity. Dimensions of a physical quantity are the powers to which the base quantities are to be raised to represent that quantity. Physical quantities like mass, length, time, etc. can be expressed in terms of dimensions. The total error of a quantity can be calculated by summing up the errors in the base quantities.

**Formula used:**

$\dfrac{{\Delta x}}{x} \times 100 = \dfrac{{\Delta M}}{M} \times 100 + \dfrac{{\Delta L}}{L} \times 100 + \dfrac{{\Delta T}}{T} \times 100$

Where ${\text{ }}\dfrac{{\Delta x}}{x} \times 100{\text{ }}$is the percentage error in the physical quantity

${\text{ }}\dfrac{{\Delta M}}{M} \times 100{\text{ }}$ stands for the percentage error in the mass (${\text{ }}M{\text{ }}$)

${\text{ }}\dfrac{{\Delta L}}{L} \times 100{\text{ }}$ stands for the percentage error in the length (${\text{ }}L{\text{ }}$)

and, ${\text{ }}\dfrac{{\Delta T}}{T} \times 100{\text{ }}$ stands for the percentage error in the time (${\text{ }}T{\text{ }}$)

**Complete step by step solution:**

All physical quantities can be expressed as a combination of fundamental or base quantities. The seven fundamental quantities as Mass (${\text{ }}M{\text{ }}$), Length (${\text{ }}L{\text{ }}$), Time (${\text{ }}T{\text{ }}$), Electric current${\text{ }}\left( A \right){\text{ }}$, Thermodynamic temperature${\text{ }}\left( K \right){\text{ }}$, Luminous intensity, ${\text{ }}(cd){\text{ }}$ and Amount of substance${\text{ }}\left( {mol} \right){\text{ }}$

We can write the dimension of any physical quantity by putting the suitable powers to the base quantities that represent that quantity.

When we use an instrument to measure a quantity, the measured value will be different from its true value. The difference between the measured value and the true value is called the error.

The percentage error in measuring${\text{ }}M{\text{ }}$,${\text{ }}\dfrac{{\Delta M}}{M} \times 100{\text{ }}$${\text{ }} = 1\% {\text{ }}$

The percentage error in measuring${\text{ }}L{\text{ }}$,${\text{ }}\dfrac{{\Delta L}}{L} \times 100{\text{ }}$${\text{ }} = 1.5\% $

The percentage error in measuring, ${\text{ }}T$${\text{ }}\dfrac{{\Delta T}}{T} \times 100$=${\text{ }}3\%.$

The percentage error in the physical quantity with dimension ${\text{ }}\left[ {M{L^{ - 1}}{T^{ - 1}}} \right]{\text{ }}$can be obtained by substituting these values in the equation,

$\dfrac{{\Delta x}}{x} \times 100 = \dfrac{{\Delta M}}{M} \times 100 + \dfrac{{\Delta L}}{L} \times 100 + \dfrac{{\Delta T}}{T} \times 100$

Substituting the values in the equation,

$\dfrac{{\Delta x}}{x} \times 100$$ = 1 + 1.5 + 3$

$\dfrac{{\Delta x}}{x} \times 100 = 5.5\% $

**The answer is Option (E):${\text{ }}5.5\%.$**

**Note:**Percentage error is the relative error expressed in percentage. The dimensional formula of a given physical quantity is an expression showing the dimensions of the fundamental quantities. An equation connecting the physical quantity with its dimensional formula is called the dimensional equation of that physical quantity.

Recently Updated Pages

If a wire of resistance R is stretched to double of class 12 physics JEE_Main

Let f be a twice differentiable such that fleft x rightfleft class 11 maths JEE_Main

Find the points of intersection of the tangents at class 11 maths JEE_Main

For the two circles x2+y216 and x2+y22y0 there isare class 11 maths JEE_Main

The path difference between two waves for constructive class 11 physics JEE_MAIN

What is the difference between solvation and hydra class 11 chemistry JEE_Main

Other Pages

In order to convert Aniline into chlorobenzene the class 12 chemistry JEE_Main

A closed organ pipe and an open organ pipe are tuned class 11 physics JEE_Main

The correct order increasing acidic strength is A Phenol class 12 chemistry JEE_MAIN

The mole fraction of the solute in a 1 molal aqueous class 11 chemistry JEE_Main

Which of the following is not a redox reaction A CaCO3 class 11 chemistry JEE_Main

Assertion The melting point Mn is more than that of class 11 chemistry JEE_Main